Problem: Simplify the following expression: ${3(k+7)-5(-6+3k)}$
Answer: Distribute the ${3}$ into the first set of parentheses: $ {3(}\gray{k+7}{)} - 5(-6+3k) $ $ {3k+21} - 5(-6+3k) $ Distribute the ${-5}$ into the parentheses: $ 3k+21 {-5(}\gray{-6+3k}{)} $ $ 3k+21 + {30-15k} $ Rewrite the expression to group the ${k}$ terms and numeric terms: $ {3k - 15k} + {21 + 30}$ Combine the ${k}$ terms: $ {-12k} + {21 + 30}$ Combine the numeric terms: $ {-12k} + {51}$ The simplified expression is $-12k+51$